The French historian Auguste Bouché-Leclercq made major contributions to our knowledge of the Hellenistic period. A member of the Académie des Inscriptions et Belles-Lettres, he was also made an officer of the Légion d'Honneur. Bouché-Leclercq is also considered the first modern historian of astrology: he had developed a long-lasting interest in divination during his extensive researches on ancient Greek civilisation. This field had not been considered worthy of serious scholarly study until he published his Histoire de la divination (...) dans l'antiquité between 1879 and 1882. L'Astrologie grecque, first published in 1899, is another important work, still referred to today. Bouché-Leclercq looks back to the oriental roots of Greek astrology. He delves into the specific influence of the zodiac signs, and explains how the celestial sphere was divided in order to draw horoscopes. Other topics include astrology in Roman culture, as well as astrological medicine. (shrink)

La lecture de Bernard de Clairvaux fut déterminante pour Blondel, spécialement dans la genèse de sa phénoménologie de l'action. En reconnaissant cette dette, le philosophe allait contre une opinion généralement reçue. Au lieu de rechercher, dans l'œuvre du moine du XIIe siècle, une redoutable critique de la " philosophie ", Blondel y déchiffrait une véritable anthropologie. Une rencontre féconde! A l'aide de documents inédits, Jean Leclercq repère les lieux philosophiques où Maurice Blondel s'est laissé inspirer par le génial cistercien (...) et, dans une lecture croisée, il identifie leurs lignes de convergence. Cette mise en abyme des deux pensées révèle leur actualité : l'action est la manifestation d'une quête de sens et d'unité. Elle est aussi le lieu d'une liberté qui se cherche, pour s'affirmer, par-delà les déterminismes de la vie et de la pensée. (shrink)

According to the deductivist view of mathematics which became the rule during the nineteenth century, formal proofs working with symbolic formulas replaced the intuitive knowledge that used to be gained by the step-by-step construction of geometric fgures and diagrams. Twentieth century epistemological refection on symbolic formulas and formal proofs, however, took them to be diagrams respectively exhibiting formal relations and transformations. The claim was also made that, for such diagrams to be proofs, temporal displays of transformations—and of other speech acts—were (...) required. By returning to the signifcant elements of contemporary theories of mathematical proofs, we will here show how these proofs came to be a matter for semiotics and pragmatics as much as for formal logic. Once this is done, we will provide a few arguments against the standard objections to the ability of diagrams to present temporal order or perform speech acts. (shrink)

Stefan Collini challenges the common claim that universities need to show that they help to make money in order to justify getting more money.

We argue for an intimate relation between semantic externalism and semantic deference and propose a typology of speakers’ metasemantic views as revealed by their deferential attitudes. Building on this typology, we then offer a classification of metasemantic disagreements understood as verbal disputes between speakers who (consciously or unconsciously) hold divergent metasemantic views about the same word. In particular, we distinguish lower-order metasemantic disagreements between speakers who disagree on the exact source of meaning determination for a word yet agree on the (...) kind of deferential attitude this word is liable to, from higher-order metasemantic disagreements between speakers who do not even agree on the suitable kind of deferential attitude. We demonstrate the fruitfulness of our classification through the concrete implications it has for conceptual engineering. (shrink)

In the following paper we provide a personal definition of the existential philosophy and the existential subject. Before that we explore other historical definitions of existentialism. We were mainly interested in the relation between existentialism and nihilism, the focus of existential philosophy on the individual and the situation of the studied philosophical trend on the 1950's zeitgeist. The definition of existentialism as a form of trans-rationalism and its capacity to become a practical alternative to contemporary academic philosophy were also emphasized.

Mi meta en este trabajo es proponer un nuevo tipo de argumento en defensa del ideal deliberativo de reciprocidad de justificación —que fue inicialmente introducido por el liberalismo político de John Rawls—. Dicho argumento aspira a demostrar que, aun cuando aceptemos la hipótesis de que un grupo de ciudadanos dispone de una justificación pública apropiada para creer que determinada doctrina comprehensiva es verdadera o correcta, existen razones morales fundamentales para rechazar la pretensión de que el estado pueda estar justificado para (...) actuar sobre la base de esas creencias cuando las esencias constitucionales o cuestiones de justicia básica se encuentran en juego. (shrink)

Explainable artificial intelligence (XAI) aims to help people understand black box algorithms, particularly of their outputs. But what are these explanations and when is one explanation better than another? The manipulationist definition of explanation from the philosophy of science offers good answers to these questions, holding that an explanation consists of a generalization that shows what happens in counterfactual cases. Furthermore, when it comes to explanatory depth this account holds that a generalization that has more abstract variables, is broader in (...) scope and/or more accurate is better. By applying these definitions and contrasting them with alternative definitions in the XAI literature I hope to help clarify what a good explanation is for AI. (shrink)

Artificial Intelligence (AI) is increasingly adopted in society, creating numerous opportunities but at the same time posing ethical challenges. Many of these are familiar, such as issues of fairness, responsibility and privacy, but are presented in a new and challenging guise due to our limited ability to steer and predict the outputs of AI systems. This chapter first introduces these ethical challenges, stressing that overviews of values are a good starting point but frequently fail to suffice due to the context (...) sensitivity of ethical challenges. Frequently, additional (ethical) values emerge for specific applications, as e.g. challenges with fraud detection are very different from those around language technologies. Second, methods to tackle these challenges are discussed. Main ethical theories (virtue ethics, consequentialism, and deontology) are shown to provide a starting point, but often lack the details needed for actionable AI Ethics. Instead, mid-level philosophical theories coupled to design-approaches such as Design for Values, together with interdisciplinary working methods, offer the best way forwards. The chapter aims to show how these approaches can lead to an ethics of AI that is actionable and that can be proactively integrated in the design of AI systems. (shrink)

This imaginative and unusual book explores the moral sensibilities and cultural assumptions that were at the heart of political debate in Victorian and early twentieth-century Britain. It focuses on the role of intellectuals as public moralists and suggests ways in which their more formal political theory rested upon habits of response and evaluation that were deeply embedded in wider social attitudes and aesthetic judgments. Collini examines the characteristic idioms and strategies of argument employed in periodical and polemical writing, and reconstructs (...) the sense of identity and of relation to an audience exhibited by social critics from John Stuart Mill and Matthew Arnold to J.M. Keynes and F.R. Leavis. (shrink)

El debate entre liberalismo y perfeccionismo ha sido uno de los ejes centrales de la Filosofía política durante los últimos veinte años. Este libro aspira a analizar críticamente y, en última instancia, a ofrecer una defensa del núcleo conceptual de la posicíon liberal. A lo largo del trabajo, se examina y discute una amplia serie de argumentos propuestos por filósofos contemporáneos "Rawls, Larmore, Barry, Kymlicka, Nagel y Ackerman, entre otros" en defensa de la neutralidad estatal. A su vez, se desarrollan (...) dos líneas de argumentacíon en defensa de las posiciones liberales que pretenden superar las falencias analizadas a lo largo del libro. La meta del primer argumento es demostrar que quien acepte las ideas fundamentales de la cultura política de las democracias contemporáneas deberá aceptar también las ideas básicas del liberalismo. Su punto de partida es una formulacíon del ideal ético-político de igual respeto por las personas y una reinterpretacíon y ampliacíon de lo que Rawls ha denominado las "cargas del juicio". El segundo argumento toma como punto de partida una idea arraigada en la tradicíon de pensamiento liberal: la necesidad de reconocer la falibilidad humana y sus consecuencias políticas y morales. El argumento combina la apelacíon a una premisa falibilista con una distincíon entre razones para afirmar una creencia y razones para estar justificado a actuar a partir de ella en contextos en los que cometer un error acarrearía un daño grave a terceros. Sobre esta base, se señala una serie de ventajas de las políticas que satisfacen los requisitos de justificacíon neutrales frente a las políticas perfeccionistas. (shrink)

Why is John Dewey still such an important philosopher today? Writing from the perspective of the Cologne Program of Interactive Constructivism, Stefan Neubert tries in what follows to give one possible answer to this question. Neubert notes that Cologne constructivism considers Dewey in many respects as one of the most important predecessors of present-day constructivism and regards Deweyan pragmatism as one of its most important dialogue partners in contemporary discussions about pragmatism and constructivism in philosophy and education. Among the many (...) aspects in which Dewey's works still speak powerfully to us today, Neubert highlights in this essay one theme that is at the heart of Dewey's philosophical approach: the relation between democracy and education. (shrink)

En mai 2007, une «table ronde» s’est tenue, au Collège International de Philosophie à Paris, autour de l’ouvrage de Pierre Magnard Pourquoi la religion?. Dans un texte récapitulatif, l’auteur du livre, spécialiste de la pensée de la Renaissance, montre les enjeux spéculatifs et pratiques de son approche de la religion, tout en exposant comment celle-ci se déploie dans la «marche» des hommes, en souci de leur humanisation. Si la religion – terme qu’il faut entendre ici au singulier – fait oeuvre (...) de reliaison, apportant sa contribution au fondement du lien social, n’est-ce pas en raison de sa vertu déliante: «seule la religion rassemble dûment, car elle seule est capable de délier»? Jean Leclercq donne une présentation des lignes de faîte de l’ouvrage, ce qui permet d’en prendre une première connaissance et de suivre les trois lectures, accompagnées de questionnements, que proposent ensuite, selon des perspectives différentes et complémentaires, Bernard Bourgeois, Thierry Gontier et Christian Trottmann. (shrink)

El presente artículo propone algunas objeciones contra la concepción deliberativa de la democracia desarrollada por Carlos Nino. El blanco central de las objeciones es la tesis del filósofo argentino según la cual el valor del debate democrático derivaría, fundamentalmente, de sus virtudes epistémicas, es decir, de su capacidad para elevar las probabilidades de que el sistema político tome las decisiones correctas. Se cuestiona el modo en que el autor presenta su propuesta como una forma de superar las deficiencias que presentarían (...) las concepciones de John Rawls y Jürgen Habermas en el campo de la epistemología moral. Se intentará demostrar que el modelo de deliberación defendido por Nino no resulta aplicable a un contexto de pluralismo razonable filosófico, religioso y moral como el que resulta característico de las democracias liberales contemporáneas. Por último, se ofrece el esbozo de una concepción alternativa, práctica y moral, no epistémica, del valor de los procedimientos democráticos y de la naturaleza de la legitimidad política. This paper posits some objections against the deliberative conception of democracy developed by Carlos Nino. According to Nino, the value of democratic deliberation lies, basically, in its epistemic virtues. Public deliberation increases the probability that the political system will arrive at the correct decisions. We shall argue that the Argentinean philosopher fails to prove that his proposal is a solution to purported weaknesses in John Rawls’ and Jürgen Habermas’ positions in the field of moral epistemology. We shall try to demonstrate that the conception of deliberation posited by nino cannot be applied successfully in the context of moral, philosophical or religious reasonable pluralism that characterizes liberal contemporary democracies. Finally, we offer an outline of an alternative conception -practical and moral, non epistemic- of the value of democratic procedures and about the nature of political legitimacy. (shrink)

La meta del presente artículo es probar que existen contextos de acción en los que tiene lugar una escisión entre el conocimiento moral de los sujetos y la justificación, también moral, de sus acciones. Para que ello ocurra, según sostendremos, deben darse al menos dos condiciones: el costo de actuar sobre la base de creencias falsas debe ser muy elevado para el bienestar de los afectados y la probabilidad de que tal resultado se produzca efectivamente, aunque baja, debe ser significativa (...) o no trivial. Sostendremos que la escisión entre conocimiento y justificación de la acción referida tiene importantes consecuencias para la estructura de la deliberación moral. This paper is aimed at proving that in certain contexts of action there may be a cleavage between the moral knowledge of an agent and the moral justification of her actions. I will argue that this is so when two conditions obtain: first, acting on the basis of false beliefs may end-up being very costly in terms of the welfare of those affected; and second, even if low, the probability of such negative upshots are significant or not trivial. I shall claim that this cleavage between knowledge and justification of actions has important consequences for the structure of moral deliberation. (shrink)

La meta del presente artículo es defender la tesis de que la aceptación de las ideas fundamentales del liberalismo político no conducen necesariamente a una concepción de la justicia global minimalista como la que desarrolló John Rawls en The Law of Peoples. Sostendré, contra lo que el filósofo explícitamente afirma, que las democracias liberales contemporáneas pueden apelar públicamente, en la esfera política global, a los ideales igualitarios y a una concepción robusta de los derechos humanos como justificación de ciertos aspectos (...) de su política exterior. Intentaré demostrar que ello no resulta incompatible con el requisito de asumir una posición de tolerancia y de respeto con las naciones que suscriben mayori-tariamente formas de vida y sistemas de creencias incompatibles con algunos de los valores liberales más significativos. The purpose of the following article is to sustain the view that accepting the basic notions of political liberalism does not necessarily lead to a minimalistic concept of global justice as that developed by John Rawls in The Law of Peoples. In opposition to his explicit opinion, I shall hold that -within the global political field- contemporary liberal democracies can publicly hold egalitarian ideals and a robust conception of human rights in order to justify some of the features of their foreign policy. I shall try to demonstrate that this is not incompatible with the required tolerance and respect toward nations that conspicuously embrace ways of life and belief systems incompatible with some of the most relevant liberal values. (shrink)

En A Letter Concerning Toleration John Locke argumenta en favor de la tolerancia religiosa afirmando que el Estado no puede mejorar la vida de las personas forzándolas a vivir de acuerdo con creencias que ellas no suscriben. Más recientemente, Ronald Dworkin y Will Kymlicka han desarrollado argumentos similares. En el caso del primero, contra ciertas políticas paternalistas; en el del segundo, en apoyo de la tesis liberal de la neutralidad estatal. Mi propósito en el presente artículo es analizar la plausibilidad (...) de dichos argumentos concebidos como una defensa de la tesis de la neutralidad estatal. Intentaré demostrar que ambas versiones del argumento fracasan. En la sección II, cuestionaré la capacidad de los argumentos para respaldar las conclusiones que aspiran establecer, sin objetar la plausibilidad de las premisas involucradas. En la sección III, desarrollaré tres objeciones contra la concepción del bienestar crítico que constituye el corazón de ambas versiones del argumento. In A Letter Concerning Toleration, John Locke argues in favor of religious toleration positing that the state cannot make a person's life better by forcing that person to live according to beliefs he refuses. More recently, Ronald Dworkin and Will Kymlicka have developed similar arguments. In the first case, against some paternalistic policies; in the second, in support of the liberal ideal of state neutrality. My aim in the present paper is to analyze the plausibility of these arguments conceived as a defense of liberal neutrality. I will prove that both versions of the argument fail. In section II, I will object the argument's capability to support the conclusions it attempts to establish, without raising doubts about the reliability of its premises. In section III, I will submit three objections against the conception of critical well-being that constitutes the core of both versions of the argument. (shrink)

RESUMEN Los defensores del liberalismo político sostienen que el ejercicio del poder político es legítimo solo cuando es justificado por razones públicas que todos los ciudadanos pueden aceptar con independencia de la doctrina religiosa, filosófica o moral a la que se adhieren. Según John Rawls, satisfacer esa concepción de la legitimidad exige apelar, en la justificación pública de la acción del Estado, a "concepciones políticas de la justicia". Se busca elaborar un nuevo tipo de argumento a favor de la posición (...) de Rawls. ABSTRACT The supporters of political liberalism hold that the exercise of political power is legitimate only when it is justified by public reasons acceptable to all citizens, independently of the religious, philosophical, or moral doctrine they adhere to. In John Rawls' view, satisfying this conception of legitimacy makes it necessary to appeal to "political conceptions of justice" when attempting to publicly justify actions by the State. The article sets forth a new type of argument in favor of Rawls' position. RESUMO Os defensores do liberalismo político sustêm que o exercício do poder político é legítimo só quando é justificado por razões públicas que todos os cidadãos podem aceitar com independência da doutrina religiosa, filosófica ou moral à qual se aderem. Segundo John Rawls, satisfazer essa concepção da legitimidade exige apelar, na justificativa pública da ação do Estado, a "concepções políticas da justiça". Procura-se elaborar um novo tipo de argumento a favor da posição de Rawls. (shrink)

How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...) initial segment of the natural numbers on the basis of the Fregean definitions, but do not learn the natural number structure as a whole on the basis of Hume's principle. Therefore, we need to account for some of the consistency of our number concepts with the Dedekind-Peano axioms in other terms. (shrink)

Sur la décomposition des ensembles de points en parties respectivement congruentes.

Can concepts be acquired by testing hypotheses about these concepts? Fodor famously argued that this is not possible. Testing the correct hypothesis would require already possessing the concept. I argue that this does not generally hold for mathematical concepts. I discuss specific, empirically motivated, hypotheses for number concepts that can be tested without needing to possess the relevant number concepts. I also argue that one can test hypotheses about the identity conditions of other mathematical concepts, and then fix the application (...) conditions based on those hypotheses—under the assumption that the neo‐logicist view on abstraction principles is correct. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

Process reliabilist accounts claim that a belief is justified when it is the result of a reliable belief-forming process. Yet over what range of possible token processes is this reliability calculated? I argue against the idea that _all_ possible token processes (in the actual world, or some other subset of possible worlds) are to be considered using the case of a user acquiring beliefs based on the output of an AI system, which is typically reliable for a substantial local range (...) but unreliable when all possible inputs are considered. I show that existing solutions to the generality problem imply that these cases cannot be solved by a more fine-grained typing of the belief-forming process. Instead, I suggest that reliability is evaluated over a range restricted by the content of the actual belief and by the similarity of the input to the actual input. (shrink)

We provide a number of simplified and improved separations between pairs of Resolution-with-bounded-conjunction refutation systems, Res, as well as their tree-like versions, Res⁎. The contradictions we use are natural combinatorial principles: the Least number principle, LNPn and an ordered variant thereof, the Induction principle, IPn.LNPn is known to be easy for Resolution. We prove that its relativization is hard for Resolution, and more generally, the relativization of LNPn iterated d times provides a separation between Res and Res. We prove the (...) same result for the iterated relativization of IPn, where the tree-like variant Res⁎ is considered instead of Res.We go on to provide separations between the parameterized versions of Res and Res. Here we are able again to use the relativization of the LNPn, but the classical proof breaks down and we are forced to use an alternative. Finally, we separate the parameterized versions of Res⁎ and Res⁎. Here, the relativization of IPn will not work as it is, and so we make a vectorizing amendment to it in order to address this shortcoming. (shrink)

This article shows how activists in the open data movement re-articulate notions of democracy, participation, and journalism by applying practices and values from open source culture to the creation and use of data. Focusing on the Open Knowledge Foundation Germany and drawing from a combination of interviews and content analysis, it argues that this process leads activists to develop new rationalities around datafication that can support the agency of datafied publics. Three modulations of open source are identified: First, by regarding (...) data as a prerequisite for generating knowledge, activists transform the sharing of source code to include the sharing of raw data. Sharing raw data should break the interpretative monopoly of governments and would allow people to make their own interpretation of data about public issues. Second, activists connect this idea to an open and flexible form of representative democracy by applying the open source model of participation to political participation. Third, activists acknowledge that intermediaries are necessary to make raw data accessible to the public. This leads them to an interest in transforming journalism to become an intermediary in this sense. At the same time, they try to act as intermediaries themselves and develop civic technologies to put their ideas into practice. The article concludes with suggesting that the practices and ideas of open data activists are relevant because they illustrate the connection between datafication and open source culture and help to understand how datafication might support the agency of publics and actors outside big government and big business. (shrink)

ABSTRACT How do non-experts single out numbers for reference? Linnebo has argued that they do so using a criterion of identity based on the ordinal properties of numerals. Neo-logicists, on the other hand, claim that cardinal properties are the basis of individuation, when they invoke Hume’s Principle. I discuss empirical data from cognitive science and linguistics to answer how non-experts individuate numbers better in practice. I use those findings to develop an alternative account that mixes ordinal and cardinal properties to (...) provide a detailed answer to the question: how do we in fact semantically individuate numbers? (shrink)

Integrating the study of human diversity into the human evolutionary sciences requires substantial revision of traditional conceptions of a shared human nature. This process may be made more difficult by entrenched, 'folkbiological' modes of thought. Earlier work by the authors suggests that biologically naive subjects hold an implicit theory according to which some traits are expressions of an animal's inner nature while others are imposed by its environment. In this paper, we report further studies that extend and refine our account (...) of this aspect of folkbiology. We examine biologically naive subjects' judgments about whether traits of an animal are 'innate', 'in its DNA' or 'part of its nature'. Subjects do not understand these three descriptions to be equivalent. Both innate and in its DNA have the connotation that the trait is species-typical. This poses an obstacle to the assimilation of the biology of polymorphic and plastic traits by biologically naive audiences. Researchers themselves may not be immune to the continuing pull of folkbiological modes of thought. (shrink)

Linsky and Zalta try to explain how we can refer to mathematical objects by saying that this happens through definite descriptions which may appeal to mathematical theories. I present two issues for their account. First, there is a problem of finding appropriate pre-conditions to reference, which are currently difficult to satisfy. Second, there is a problem of ensuring the stability of the resulting reference. Slight changes in the properties ascribed to a mathematical object can result in a shift of reference (...) and this leads to various problems, e.g., it makes inferring knowledge much harder than it is. (shrink)

The normative mechanics of promising seem complex. The strength and content of promissory obligations, and the residual duties they entail upon being violated, have various prima facie surprising features. We give an account to explain these features. Promises have a point. The point of a promise to φ is a promise-independent reason to φ for the promisee’s sake. A promise turns this reason into a duty. This explains the mechanics of promises. And it grounds a nuanced picture of immoral promises, (...) an argument against promissory bare wrongings, and a constraint on theories of why we have promissory obligations at all. (shrink)

We are currently witnessing the emergence of a ‘third culture’, driven by unprecedented developments that are changing the playing field. These include advances in AI, big data analysis and robotics. The traditional ‘two cultures’ view (S. P. Snow) distinguishes between the sciences and the humanities. The wisdoms these two cultures offer are separated from each other, with little to no interaction or mutual comprehension. However, over the past two decades, and for the first time in human history, a new, third (...) culture has appeared. This new culture, rooted in new technologies, not only pursues its own form of rationality but also supports advances in the original two cultures, deepening and expanding our individual and collective consciousness so that we can see more and do better. It will eventually give rise to new forms of consciousness based not on biochemical signals, but on copper wires and lithium chips. These new machine intelligences will change the world and force us to realise: we are no longer alone. The human species’ position in the twenty-first century will be fundamentally redefined: not as a conductor leading the orchestra, but a single string player within it. (shrink)

Ziel dieses Aufsatzes ist es, Robert Brandoms Begriff des Explizit-Machens explizit zu machen. Zu diesem Zweck werden zunächst verschiedene Formen des Explizit-Machens unterschieden. Dabei erweist sich allein der Begriff des logischen Explizit-Machens als haltbar. Anschließend wird gezeigt, dass diesem Begriff eine Schlüsselstellung im Rahmen von Brandoms Philosophie zukommt. Sowohl seine philosophische Methodologie als auch sein zentrales philosophisches Projekt einer Zurückführung von Semantik auf Pragmatik lassen sich höchstens soweit verständlich machen wie der Begriff des logischen Explizit-Machens. Dieser weist allerdings ein erhebliches (...) Defizit auf: Im Rahmen einer Inferentialistischen Semantik lässt sich die expressive Funktion wichtiger Teile des logischen Vokabulars nicht verständlich machen. Das Ergebnis ist, dass sich zwei der Grundpfeiler von Brandoms Sprachphilosophie, die Inferentialistische Semantik einerseits und deren Zurückführung auf eine normative Pragmatik andererseits, nicht gleichzeitig konsequent durchhalten lassen. (shrink)

To understand Nietzsche's view of education requires us to grasp the importance Nietzsche attaches to being embedded in a particular historical and cultural frame. Education is, at least in the early stages, a matter of teaching the child to see and to value particular things or, in Nietzsche's way of putting this, teaching the child to lie. Here I develop an interpretation contrary to those who emphasise Nietzsche's radical individualism and thus view his Overman in subjectivistic terms. I argue that (...) Nietzsche's most important lesson is not that we are to create anything radically new, but rather that we are to take up a serious engagement with respect to what we stand for. (shrink)

Most accounts of our knowledge of the successor axiom claim that this is based on the procedure of adding one. While they usually don’t claim to provide an account of how children actually acquire this knowledge, one may well think that this is how they get that knowledge. I argue that when we look at children’s responses in interviews, the time when they learn the successor axiom and the intermediate learning stages they find themselves in, that there is an empirically (...) viable alternative. I argue that they could also learn it on the basis of a method that has to do with the structure of the numeral system. Specifically, that they (1) use the syntactic structure of the numeral system and (2) attend to the leftmost digits, the one with the highest place-value. Children can learn that this is a reliable method of forming larger numbers by combining two elements. First, a grasp of the syntactic structure of the numeral system. That way they know that the leftmost digit receives the highest value. Second, an interpretation of numerals as designating cardinal values, so that they also realise that increasing or adding digits on the lefthand side of a numeral produces a larger number. There are thus two, currently equally well-supported, ways in which children might learn that there are infinitely many natural numbers. (shrink)